What is the relationship between the universal gravitational constant (G) and the acceleration due to
gravity (g)?- question from Kashim Grema

The universal constant of gravitation (G) is an important variable frequently used in fields like orbital mechanics
where it plays a role in calculating parameters such as orbital speed.
Acceleration due to gravity (g) is also an important variable used to
calculate properties like speed near the surface of a planet or other large
body.

The value of G is a constant that should not change no matter where one is in the universe. The value of g,
however, does vary for each planet, star, moon, or other large body based on its size and mass. These two
gravitational parameters are related by the equation:

G = 6.673 x 10-11 m³/kg/s² in the Metric system
G = 3.439 x 10-8 ft³/slug/s² in the English system

Using this relationship, we can solve for the acceleration due to gravity on any planet so long as we know the
planet's size. The acceleration due to gravity of Earth, for example, is known to be about 9.81 m/s² or
32.2 ft/s². Let us verify this value by plugging the Earth's mass (ME) and radius (RE) into
the above equation.

ME = 5.98 x 1024 kg in the Metric system
ME = 4.094 x 1023 slugs in the English system

RE = 6.375 x 106 m in the Metric system
RE = 2.091 x 107 ft in the English system

When we do so, we find that the Earth's acceleration due to gravity is indeed about 9.81 m/s².

Scale drawing of the relative sizes of planets and moons in the solar system

We can go even further by using this relationship to solve for the acceleration due to gravity on other planets or
moons. The following table provides the mass, radius, and gravitational acceleration of several major bodies
within our solar system.

Acceleration Due to Gravity Comparison

Body

Mass [kg]

Radius [m]

Acceleration Due to Gravity, "g" [m/s²]

g / g-Earth

Sun

1.99 x 1030

6.96 x 108

274.13

27.95

Mercury

3.18 x 1023

2.43 x 106

3.59

0.37

Venus

4.88 x 1024

6.06 x 106

8.87

0.90

Earth

5.98 x 1024

6.38 x 106

9.81

1.00

Moon

7.36 x 1022

1.74 x 106

1.62

0.17

Mars

6.42 x 1023

3.37 x 106

3.77

0.38

Jupiter

1.90 x 1027

6.99 x 107

25.95

2.65

Saturn

5.68 x 1026

5.85 x 107

11.08

1.13

Uranus

8.68 x 1025

2.33 x 107

10.67

1.09

Neptune

1.03 x 1026

2.21 x 107

14.07

1.43

Pluto

1.40 x 1022

1.50 x 106

0.42

0.04

The last column of the table compares the acceleration due to gravity of the body to that of Earth. A small body
like the Moon only exerts a gravitational acceleration about 1/6th as strong as that of Earth while the massive Sun
generates an acceleration nearly 28 times that of Earth. Tiny Pluto, meanwhile, only exerts about 4% the gravity
of Earth.

This information is also useful since it directly corresponds to how much an object would weigh on the surface of
each of these bodies. We have previously discussed the relationship between weight, mass, and gravity in a
number of articles. As we have seen, the mass of an object remains constant whether it is on the surface of Earth,
the surface of the Moon, or in the depths of space. The quantity that does change depending on the strength of the
gravitational field is the object's weight. These variables are related by the equation:

Since we now know the acceleration due to gravity on different worlds, we can easily determine how much an object
weighs on those bodies. We have shown that the value of "g" on the Moon is 1/6th that of Earth, so an object on
the Moon weighs only 1/6th as much as it would on Earth. A person weighing 150 pounds on Earth, for example, would
weigh only 25 pounds on the Moon.

Another place in the solar system humans are likely to visit in the future is Mars. Although Mars is the planet
most like Earth in terms of its environment, the gravitational acceleration on this much smaller planet is only
about 40% that of Earth. Mars is also farther from the Sun and takes longer to complete an orbit, so a Martian
year is about twice as long as a year on Earth. On this Mother's Day, you might consider offering the women in
your life a trip to the distant red planet. After all, what woman wouldn't like the idea of having her weight and
age cut in half?!
- answer by Joe Yoon, 8 May 2005